TACHS Practice Questions (2026) — Free Sample Questions with Answers

Answer: A

They supported his interest even when it was costly: Correct — his mother gave him a microscope (paragraph 2), and his parents bought him a camera "although money was tight on the farm" (paragraph 3).

They hoped he would someday become a famous scientist: The passage shows support but never says what career they wanted for him.

They wanted him to spend more time farming: Confuses the parents with the neighbors, who laughed at him (paragraph 4); the parents' actions show support.

They taught him how to use a camera: The passage says he struggled for two winters on his own; it never says they taught him.

To infer a character's attitude, combine their actions across paragraphs; two gifts given despite tight money point to support.

Answer: C

Most riders quit because the work was dangerous: Paragraph 4 describes the dangers, but neither paragraph 3 nor 6 says riders quit.

Newspapers stopped paying once the war began: Not supported: the passage never says customers stopped paying.

Even high prices did not cover the costs of the service: Correct — paragraph 3 says letters were costly to send, and paragraph 6 says the service still "lost a great deal of money," so its costs were greater than its income.

The telegraph company bought the service to close it: The passage says the Pony Express closed after the telegraph line was finished, not that it was bought.

An inference must be supported by details from both paragraphs named; combine them (high prices + money lost) and see what must follow.

Answer: A

"Don't judge a book by its cover.": Correct. The beautiful bridge fails and the messy-looking one wins, and Gemma learns from the bridge the others laughed at.

"Slow and steady wins the race.": Hollis's bridge held as the bucket slowly filled, but the story is not about patience or speed.

"Two heads are better than one.": Gemma learns from Hollis, but they never work together on a bridge.

"Practice makes perfect.": Fits only the last paragraph, where she starts again; it misses the contrast between how the bridges looked and how they held.

The best saying fits the whole story; wrong choices fit only one detail.

Answer: C

Horse-drawn plows made cutting ice much faster: A single detail from paragraph 2; the passage also covers storing, selling and the end of the trade.

Factory ice was cleaner and safer than pond ice: A detail from paragraph 5 only, and the passage never mentions safety.

People once cut and stored winter ice for summer use: Correct. Every paragraph builds this idea: why ice was needed, how it was cut, kept, sold, and then replaced.

Selling ice overseas made New England towns wealthy: Paragraph 4 says ice became big business, but never says the towns grew wealthy; this overreaches one detail.

The main idea covers the whole passage, not just one paragraph.

Answer: C

Line 1: "Me" is correct: it is an object of "asked" (asked me).

Line 2: The comma after the introductory phrase "After the game" is correct.

Line 3: Correct — "I" is wrong because it is an object of "thanked"; the line should read "thanked Wen and me." Test it by dropping "Wen and": "thanked me."

No mistakes: There is a mistake in Line 3: "Wen and I" should be "Wen and me."

To choose between "I" and "me" in a pair, drop the other person and read the sentence: "thanked me," not "thanked I."

Answer: D

The Westbrook Public Library opened in 1902, it had only one room and about four hundred books.: A comma splice: two complete sentences joined only by a comma.

The Westbrook Public Library opened in 1902 and having only one room and about four hundred books.: "Opened" and "having" do not match; the sentence needs "had," not "having."

Opening in 1902, about four hundred books were in the one-room Westbrook Public Library.: Dangling modifier: "Opening in 1902" now describes the books instead of the library.

When the Westbrook Public Library opened in 1902, it had only one room and about four hundred books.: Correct — "When" turns sentence 1 into an introductory clause, and the two ideas are joined smoothly with the right time relationship.

A word such as "when" can turn one sentence into a clause that introduces the other; a comma alone cannot join two sentences.

Answer: D

Shining his flashlight under his chin, ghost stories were told by Theo in a spooky voice.: Dangling modifier: the opening phrase now describes "ghost stories," as if the stories were shining the flashlight.

Theo was shining his flashlight under his chin, he told ghost stories in a spooky voice.: A comma splice: two complete sentences joined only by a comma.

Theo told ghost stories under his chin in a spooky voice, shining his flashlight.: Misplaced modifier: "under his chin" now describes the ghost stories instead of the flashlight.

(No change): Correct — the opening phrase "Shining his flashlight under his chin" is followed directly by "Theo," the person doing the shining, so the sentence is already clear.

An opening -ing phrase must be followed right away by the person or thing doing that action; when it is, no change is needed.

Answer: A

1. Read the grid: top side = 4 units, bottom side = 8 units, height = 3 units.
2. Split the figure: a 4 × 3 rectangle (12) plus a right triangle with legs 4 and 3 (½ × 4 × 3 = 6).
3. Area = 12 + 6 = 18 square units (same as (4 + 8) ÷ 2 × 3).

18: Correct — the parallel sides are 4 and 8 units and the height is 3 units, so the area is (4 + 8) ÷ 2 × 3 = 18 square units.

20: This is the perimeter (4 + 3 + 8 + 5 = 20 units), not the area.

24: Multiplies the longer base by the height (8 × 3), counting the empty triangle beside the slanted side.

36: Adds the bases and multiplies by the height but forgets to take half: (4 + 8) × 3.

On a grid, split a figure into rectangles and right triangles, or use the trapezoid rule: half the sum of the parallel sides times the height.

Answer: D

1. Girls exceed boys by 4 − 3 = 1 part, and that difference is 6 students, so 1 part = 6.
2. Girls = 4 × 6 = 24; boys = 3 × 6 = 18.
3. Total = 24 + 18 = 42.

13: Adds the 6 to the ratio numbers (4 + 3 + 6) instead of using it to find the size of one part.

18: This is the number of boys only (3 parts × 6).

24: This is the number of girls only (4 parts × 6).

42: Correct — the difference is 4 − 3 = 1 part, so 1 part = 6 students; the club has 4 + 3 = 7 parts, and 7 × 6 = 42.

In ratio problems, use the given difference or total to find the value of one part, then multiply.

Answer: B

1. P(blue) on one pick = 3 ÷ (2 + 3 + 5) = 3/10.
2. The marble is replaced, so the second pick is also 3/10.
3. P(both blue) = 3/10 × 3/10 = 9/100.

$\frac{1}{15}$: Treats the first marble as kept out (3/10 × 2/9); it was put back.

$\frac{9}{100}$: Correct. Each pick has a 3/10 chance of blue, and with replacement 3/10 × 3/10 = 9/100.

$\frac{3}{10}$: The probability for one pick only.

$\frac{3}{5}$: Adds the two probabilities (3/10 + 3/10); for "both" events, multiply.

For "this and then that" with replacement, multiply the probabilities, which stay the same each pick.

Answer: C

1. Full rectangle: 10 × 8 = 80 square feet.
2. Missing corner: 4 × 3 = 12 square feet.
3. Area: 80 − 12 = 68 square feet (check: 6 × 8 + 4 × 5 = 48 + 20 = 68).

36 square feet: This is the perimeter of the room in feet, not its area.

60 square feet: Splits the room into 6 × 8 and 4 × 3; the right-hand piece is 4 ft wide and 8 − 3 = 5 ft tall, not 3 ft.

68 square feet: Correct. Whole rectangle 10 × 8 = 80, minus the missing 4 × 3 corner = 12, gives 68 square feet.

80 square feet: The area of the full 10 × 8 rectangle; the cut-out corner was not subtracted.

For an L-shaped figure, subtract the missing rectangle from the whole, or split it into two rectangles using the right side lengths.

Answer: C

Figure A: A hexagon has six sides, but it holds only five dots.

Figure B: Six dots, but a pentagon has only five sides.

Figure C: Correct. In each figure the number of dots inside equals the number of sides: 3 in the triangle, 4 in the square, 5 in the pentagon. Figure C is a hexagon with six dots inside.

Figure D: Three dots for three sides, but the dots are outside the triangle.

Figure E: A square with only three dots; it would need four.

When the parts change from figure to figure, look for a link between them, such as a count that matches the number of sides.

Answer: A

1. Fold 1: along the diagonal from the top-left to the bottom-right corner (2 layers, a triangle).
2. Fold 2: the triangle is folded in half along the other diagonal (4 layers, a smaller triangle on the right).
3. The punch is near the middle of the right edge.
4. Unfold fold 2: a mirror hole near the middle of the top edge.
5. Unfold fold 1: both holes are mirrored across the first diagonal, giving holes near the middle of the left and bottom edges too.

Figure A: Correct. Two diagonal folds make 4 layers. The punch sits near the middle of the right edge. Mirroring it across both diagonals gives one hole near the middle of each edge: right, top, left and bottom.

Figure B: Unfolds only the second fold: 2 holes, but the paper had 4 layers.

Figure C: Mirrors across the first diagonal only and skips the second fold: 2 holes instead of 4.

Figure D: Four holes, but at the corners, as if the folds had been straight up-and-down and across.

Figure E: The right pattern, but too close to the center; the punch was near the edge of the paper.

With two diagonal folds the holes form a pattern that looks the same from every side of the paper.

Answer: B

Figure A: Only the top-left part is white: a copy of the figure to its left, not turned again.

Figure B: Correct. Across each row the dark pattern turns one quarter clockwise. Down the columns the number of dark parts goes 1, 2, 3. In the third row the white part moves from bottom-left to top-left, so next it is top-right, with the other three parts dark.

Figure C: Only the bottom-left part is white: the pattern was turned counterclockwise.

Figure D: Two dark parts, copying the figure above; the third row has three dark parts.

Figure E: Only the bottom-right part is white: the pattern was turned two steps instead of one.

Use one rule to fix how many parts are dark and the other to fix where they are.